A polymer matrix composite comprising a porous polymeric network; and a plurality of functional particles distributed within the polymeric network structure, and wherein the polymer matrix composite has an air flow resistance at 25° C., as measured by the “Air Flow Resistance Test,” of less than 300 seconds/50 cm3/500 micrometers; and wherein the polymer matrix composite has a density of at least 0.3 g/cm3; and methods for making the same. The polymer matrix composites are useful, for example, as filters.